Quantitative models of nitrogen-fixing organisms

Abstract

Nitrogen-fixing organisms are of importance to the environment, providing bioavailable nitrogen to the biosphere. Quantitative models have been used to complement the laboratory experiments and in situ measurements, where such evaluations are difficult or costly. Here, we review the current state of the quantitative modeling of nitrogen-fixing organisms and ways to enhance the bridge between theoretical and empirical studies.

Keywords: Mathematical model; Nitrogen fixation; Nitrogen fixers; Oxygen; Photosynthesis; Quantitative model.

Graphical abstract

Fig. 1

N flows in (A) terrestrial and (B) marine systems. “N” indicates fixed N whereas “N₂” indicates dinitrogen gas.

Fig. 2

Strategies for (A) Biomass (organic) C acquisition and (B) O₂ management. Here “C” in a yellow oval represents biomass C. The following are example organisms: (A) Heterotrophic: Azotobacter, Clostridium. Photoautotrophic: Crocosphaera, Trichodesmium, Anabaena. Symbiotic: Rhizobium, UCYN-A. (B) Cellular differentiation: Anabaena, Richelia. Temporal Segregation: Crocosphaera, Cyanothece. O₂ barrier: Azotobacter (proposed , predicted and supported [81], [82]), Crocosphaera (predicted [53], [75]), Anabaena, Trichodesmium (predicted [83], [84]). Respiratory protection: Azotobacter, Crocosphaera (predicted [75], [85]), Trichodesmium (predicted [83]). Living in low O₂ environment, Clostridium. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3

Roles of quantitative models of N₂ fixers. Arrows indicate causes and effects.

Fig. 4

Schematics of three different types of models. μ_max: maximum growth rate. K: half saturation constant for growth based on nutrient concentration following Monod kinetics , widely used in ecosystem modeling , , , . Examples of coarse-grained model and detailed metabolic model include Cell Flux Model (CFM) , , , . One widely used detailed metabolic model is Flux Balance Analysis (FBA) , , , .

Fig. 5

A list of major modeled N₂ fixers and current state of model development. Checkmarks indicate that the model has been developed in each way. Numbers below the check marks are example references.

Fig. 6

Nitrogen fixers modeled by coarse-grained models and resolved elements. Checkmarks indicate that each element/parameter is simulated. O₂ indicates intracellular O₂ and fixed-N uptake indicates uptake of NH₄⁺ or NO₃⁻. Numbers below the check marks are example references.

Fig. 7

Some future applications of the physiological models of N₂ fixers. (A)-(C) Organisms that have not been quantitatively modeled. (D) Incorporating coarse-grained models into large-scale simulations. Picture for a large scale model made by Oliver Jahn.

Fig. 8

Proposed collaborative schemes between modelers and biologists when studying N₂ fixation. (A) Model-experiment cycling. (B) Experiment-model synthesis (linear flow). (A) is when model-based hypotheses are testable and (B) is when otherwise. Figure inspired by , .

Fig. 9

A list of biological experiments and data important for modeling N₂ fixation. (A) Culturing and sampling methods. (B) List of useful parameters from (A). (C) Emerging technologies that are potentially useful for the models.